Structure and Dynamics of Iron Pentacarbonyl † § ‡ § ∥ ⊥ # Peter Portius,*, , Michael Bühl, Michael W

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Cite This: Organometallics 2019, 38, 4288−4297 pubs.acs.org/Organometallics

Structure and Dynamics of Iron Pentacarbonyl † § ‡ § ∥ ⊥ # Peter Portius,*, , Michael Bühl, Michael W. George, , Friedrich-Wilhelm Grevels, , § and James J. Turner*, † Department of Chemistry, The University of Sheﬃeld, Western Bank, Sheﬃeld S3 7HF, United Kingdom ‡ School of Chemistry, University of St. Andrews, St. Andrews, Fife KY16 9ST, United Kingdom § School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom ∥ Department of Chemical and Environmental Engineering, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315100, China ⊥ Max-Planck-Institut für Bioanorganische Chemie, Stiftstraße 34-36, D-45470 Mülheim an der Ruhr, Germany

*S Supporting Information

ABSTRACT: The dynamics of CO ligand scrambling in Fe(CO)5 has been investigated by linear infrared spectroscopy in supercritical xenon solution. The activation barrier for the Berry pseudorotation in Fe(CO)5 was determined experimentally to be ± −1 Ea = 2.5 0.4 kcal mol by quantitative analysis of the temperature-dependent spectral line shape. This compares well −1 with the range of Ea/(kcal mol ) = 2.0 to 2.3 calculated by various DFT methods and the value of 1.6 ± 0.3 previously obtained from 2D IR measurements by Harris et al. (Science 2008, 319, 1820). ··· The involvement of Fe(CO)5 Xe interactions in the ligand scrambling process was tested computationally at the BP86-D3/ AE2 level and found to be negligible.

■ INTRODUCTION It is usually assumed that the mechanism involves the Berry 6 1 pseudorotation (Figure 2). Attempts to resolve the structure Since the synthesis of Fe(CO)5 in 1891, there has been a great deal of interest in its chemistry, structure, and bonding, in particular the dynamics of the scrambling of the ligands. Fe(CO)5 has a D3h-symmetric structure in the gas phase (cf. Figure 1).2 In 1958, Cotton et al.3 observed that the 13C NMR Downloaded via UNIV OF ST ANDREWS on November 12, 2019 at 16:09:29 (UTC). Figure 2. Geometries relevant for the Berry pseudorotation model of Fe(CO) and for the DFT calculations in this paper.

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have been carried out in the solid state at low temperature and have resulted in some disagreement,7,8 which is, however, of little relevance to understanding the behavior in solution. That it was possible to freeze the scrambling was shown by Turner 9 Figure 1. Ball-and-stick model of the D -symmetric structure of and colleagues using a combination of polarized photolysis 3h and IR spectroscopy in a CO matrix at 20 K. Fe(CO)5. Fe, lilac; C, gray; O, red. A large number of DFT calculations on Fe(CO)5 (and other metal carbonyls) have been carried out. Most of them were concerned with structure, and particularly with the diﬀerence spectra showed only one line at all available temperatures. − − Later work4 conﬁrmed and extended this down to −170 °C. between the axial and equatorial Fe C and C O bond lengths as well as the dissociation energy of the ligand decoordination Thus, the exchange among the CO groups must be very fast. In → rather subtle NMR experiments, Sheline and Mahnke5 reaction, Fe(CO)5 Fe(CO)4 + CO, and the vibrational estimated that at room temperature, CO scrambling occurs − at a rate of about 1.1 × 1010 s 1 with an activation energy of Received: August 16, 2019 − ∼1.13 kcal mol 1. Published: October 17, 2019

© 2019 American Chemical Society 4288 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article frequencies. Several authors have considered the energy ﬀ di erence between the D3h-symmetric ground state and the top of the barrier in the Berry mechanism (C4v). Schaefer and colleagues10 calculated the barrier height using various basis sets and obtained values of 2.25 kcal mol−1 (DZ B3LYP), 2.28 kcal mol−1 (DZP BP86), and 2.33 kcal mol−1 (DZP B3LYP) with the stated methods. In an important paper, Harris and co- workers11 estimated the barrier height to be 2.13 kcal mol−1 (BP86 with the basis sets 6-31+G(d) for C and O, and LANL2DZ for Fe). More recently, Couzijn et al.12 obtained a value of 2.0 kcal mol−1 at the B3PW91/SDD(d) level of theory. The relevance of these data will be outlined shortly. We have calculated the barrier height at the BP86, PBE, PBE0, and CCSD(T) levels of theory and obtained values between 2.0 −1 ν and 2.3 kcal mol ; see the Supporting Information (SI) for Figure 3. IR spectrum in the (CO) region of Fe(CO)5 in 2- details of the calculations. Thus, the calculation of the barrier methylpentane at −140 °C. height is remarkably independent of the DFT method. However, obtaining good experimental data for the barrier and 2 are assigned to the ν(CO) vibrations that transform as ″ ′ height and the kinetics of the Berry pseudorotation is a much the a2 and e irreducible representations of D3h-symmetric 12 more challenging problem. Fe( CO)5, respectively; those labeled 3, 4, 5, 6 arise from 13 12 The study of dynamics requires experiments to be Fe( CO)( CO)4 (see the SI for a full force constant analysis) 13 14,15 conducted over a broad range of temperatures, and with very due to naturally occurring CO. The two fundamental a′ ν small barriers in particular, one needs to be able to extend this (CO) vibrations are not active in the IR under D3h symmetry to very low ones. While there is no doubt that the structure of but become active if the symmetry is reduced slightly to C2v; the bands labeled 7 and 8 are assigned to these a′ vibrations. If Fe(CO)5 in the gas phase has D3h symmetry, the complex can undergo considerable distortion in various solvents. Elegant the distortion is considerable, the degeneracy of the e′ experiments by Rose-Petruck and colleagues13 using IR vibrations is removed. spectroscopy probed the temperature dependence of the As the temperature is raised, bands 7 and 8 disappear spectrum in the region of the ν(CO) stretches. With the because the concentration of the distorted structure decreases support of DFT calculations, they were able to show that (see Figure 4). It should also be noted that bands 5 and 6 particularly in benzene and increasingly ﬂuorinated derivatives, the structure of Fe(CO)5 distorts to C2v-orC4v-symmetric geometries. The authors also supplied thermodynamic parameters connecting the D3h structure with the various distorted structures as shown in eq 1:

Fe(CO)5 + solvent → Fe(CO)5 ··· solvent ()DCC324hvv(/) (1) In pentafluorobenzene, for instance, the parameters ΔH = −3.59 ± 0.68 kcal mol−1, ΔS = −8.43 ± 1.83 cal K−1 mol−1, and ΔG = −1.08 kcal mol−1 can be used to describe the equilibrium between the two structures at room temperature. According to these data, it can be concluded that the equilibrium lies well to the right (10.6% D3h, 89.4% C2v) and ν that the (CO) IR spectrum is dominated by the distorted ν structure. However, as the temperature is raised, and assuming Figure 4. IR spectrum in the (CO) region of Fe(CO)5 in 2- methylpentane at 20 °C. ΔH remains roughly constant, the negative entropy change will cause a shift of the equilibrium to the left. If the interaction between Fe(CO)5 and cyclohexane is presumed to be weak, it appear to have coalesced at this temperaturea fact that will is not surprising that the experimental evidence for a complex be discussed at a later stage. However, caution must be is weak, and the authors concluded that at room temperature, exercised in using even saturated hydrocarbons as supposedly “ ” 13 Fe(CO)5 is nearly undisturbed D3h in cyclohexane. With inert solvents. What solvents could be used? Figure 5 shows the negative entropy changes being involved, there will be an ff the spectra of Fe(CO)5 in liquid krypton and at two di erent even lesser distortion of the structure at higher temperatures. concentrations in liquid xenon. However, since this paper is concerned with the dynamic It is clear that even at this low temperature there is no behavior of Fe(CO)5, more information is needed about both evidence for bands 7 and 8. Under the assumption that ΔS is structures and spectra in a variety of solvents. The following ··· negative (see later), the concentrations of Fe(CO)5 Kr and describes new experimental and computational evidence for Fe(CO) ···Xe will be zero at room temperature and above. It fl 5 the barrier in this prototypical uxional molecule. will be shown later that an accurate force field is required for the investigation of the dynamics of Fe(CO) . The assignment ■ RESULTS AND DISCUSSION 5 of the energy-factored force constants of Fe(CO)5 is Figure 3 shows the ν(CO) region of the IR spectrum of straightforward and follows that of Bor.15 The details of the − ° Fe(CO)5 in 2-methylpentane at 140 C. The bands labeled 1 calculation are given in the SI. Since the experiments described

4289 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article

ﬁ ··· Figure 6. Energy pro le for Fe(CO)5 Xe as a function of the ··· Fe(CO)5 Xe distance (all other parameters optimized) calculated at the BP86/AE2 (○) (a purely repulsive potential) and BP86-D3/AE2 (●) levels.

attractive van der Waals-type dispersion interactions. Fur- thermore, in agreement with the observation made by IR spectroscopy, the optimized geometries indicate no effective ··· distortion of Fe(CO)5 (at least not until the Xe Fe(CO)5 ν distance is very small, below ca. 3.5 Å). Figure 5. IR spectra of Fe(CO)5 in the (CO) region in (a) liquid krypton at −138 °C and (b) liquid xenon at −107 °C at the The important question, however, is how the interaction ff concentrations c(b1) and c(b2) with c(b1)/c(b2) ≈ 40. could a ect the C4v-symmetric structure at the transition state − of the Berry mechanism and therefore the D3h C4v barrier in this paper were performed in liquid xenon, we provide the height. Table 2 shows the results of our DFT calculations. force constants in this medium in Table 1. a Table 2. Energy Barriers for Pseudorotation in Fe(CO)5 − ··· Table 1. C−O IR Frequencies (in cm 1) and Energy- and Fe(CO)5 Xe at the BP86-D3/AE2 Level of Theory −1 Factored Force Constants (in N m ) for Fe(CO) in Liquid b ··· 5 energy Fe(CO)5 Fe(CO)5 Xe Xe ΔE (0 K) 2.2 2.0 Frequencies ΔH (298 K) 1.6 1.4 Δ isomer band no. symmetry ν/cm−1 G (298 K) 2.9 3.2 a ff 12 ″ Evaluated as the di erence between the D3h-symmetric minimum Fe( CO)5 1a2 2023.9 2e′ 1999.6 and the C4v-symmetric transition state for Fe(CO)5 and between the 13 12 Cs-symmetric minimum shown in Figure 6 and a C4v-symmetric ax-Fe( CO)( CO)4 3a1 1988.5 ··· b transition state (not shown) for Fe(CO)5 Xe. In units of kcal − 6a1 2106.1 mol 1. 13 12 eq-Fe( CO)( CO)4 4a1 1963.2 5a2109.4 1 Only very small energy differences of 0.3 kcal mol−1 or less Force Constants were found upon evaluation of the structures of Fe(CO)5 and kax 1698.1 Xe in either the D3h or C4v geometry. It is therefore clear that in keq 1655.2 the two structures, within the limits of the calculations,16 the kax,ax 43.4 interactions between Fe(CO)5 and Xe are of a similar nature. keq,eq 39.9 Even though this calculation refers to the gas phase, in view of kax,eq 28.0 − the nature of the Xe Fe(CO)5 interaction it is unlikely that the Xe supercritical fluid environment will make a large For technical and safety reasons, it is easier to study difference to the parameters. Moreover, because the entropy Fe(CO)5 at higher temperatures in liquid Xe rather than liquid change for complex formation will be negative, the Kr. In examining the dynamical behavior of Fe(CO)5 in liquid concentration of a Xe complex at room temperature and Xe, it is worth probing the possible interaction of Fe(CO)5 above will certainly be close to zero. with Xe, particularly as the molecule distorts in the process of Obtaining good experimental data for the kinetics and barrier the Berry pseudorotation. As a first step toward modeling the height for the Berry pseudorotation is challenging. The most bulk liquid, we investigated the interaction between Fe(CO)5 direct method is to use two-dimensional infrared spectroscopy and a single Xe atom. The result of the DFT calculation (see SI (2D-IR), and this is considered here first. for details) is displayed in Figure 6 and shows how the Two-Dimensional Infrared Spectroscopy. There is an interaction energy depends on the distance between Xe and excellent book on 2D-IR by Hamm and Zanni17 and a 18 Fe(CO)5 and that the interaction is essentially caused by summary by Thielges and colleagues. The application to

4290 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article metal carbonyls has been outlined by Kubarych and the slow regime applies, and the spectrum shows two bands, colleagues,19 and a very recent review20 summarizes the each broadened by 0.1 cm−1.Ifk =1013 s−1, the fast regime experiments on metal carbonyls that have been carried out applies, and there is only a single Lorentzian profile with a over the past few years. The literature reveals that there is often width of 1/2W ≈ 1.5 cm−1. In order to observe dynamic effects a problem relating to the difficulty of distinguishing between in IR and Raman spectra, a very high exchange rate is required the effects caused by chemical exchange and those caused by (on the NMR time scale, coalescence typically occurs at k = intramolecular vibrational redistribution (IVR) (see ref 20 for a 104 s−1, but for IR bands, each would be broadened by a mere discussion of this). There is also a fundamental problem with 10−7 cm−1an effect completely unobservable with current the method by which 2D-IR monitors the exchange. 2D-IR experimental apparatus). requires excited vibrational states and records transitions However, an important point that has been emphasized in between levels at v = 1 in mode 1 and v = 1 in mode 2a several publications (see ref 20 and literature cited therein) is point emphasized by Harris.11 The Berry mechanism, however, that as the rate increases, there is increasing intensity at the assumes transfer between v = 0 states, and this point will be midpoint between two absorption bands, greater than that due elaborated at a later stage. to the change in width of the overlapping Lorentzian profiles. Harris and colleagues carried out elegant 2D-IR experiments Indeed, in the early days of NMR spectroscopy, before the on Fe(CO)5 in n-dodecane solution. Assuming the Berry advent of dynamic NMR computer programs, this extra mechanism to be operational, they obtained time constants of intensity buildup was used to estimate exchange rates.21 8.0 ± 0.6 ps at 18 °C, 6.3 ± 0.8 ps at 50 °C, and 4.6 ± 0.4 ps at The coalescence effect in vibrational spectra is well- 90 °C, which translate into rate constant values of 1.2 × 1011, illustrated in experiments by Kim and Hochstrasser,22 who × 11 × 11 −1 − 1.6 10 , and 2.2 10 s , respectively. From an Arrhenius investigated the equilibrium between free CH3CN (C N plot, the activation energy was calculated to be 1.6 ± 0.3 kcal stretch at 2254 cm−1) and H-bonded CH CN (2263 cm−1)in − 3 mol 1, which is reasonably close to the range of DFT values methanol solution. These experiments are also significant − (2.0 to 2.2 kcal mol 1, including Harris’s value of 2.13 kcal because the authors compare the FTIR data with data from − mol 1). The calculations of barrier height, however, ignore 2D-IR experiments; the kinetic results are similar. The first zero-point energies. The calculated zero-point energies of D3h evidence for this type of behavior in metal carbonyls was −1 23,24 and C4v structures are 25.9 and 25.8 kcal mol , respectively obtained by Grevels and co-workers during studies of the (BP86-D3/AE2 level, this work), meaning that the inclusion of ν(CO) absorption bands in the IR spectra of iron(tricarbonyl)- zero-point energies would only reduce the barrier by diene complexes, Fe(CO)3(diene) (see Figure 7). approximately 0.1 kcal mol−1. In addition, Harris showed convincingly11 that the vibrational transfer was not caused by IVR. Although 2D-IR is the most direct way of measuring the dynamics of exchange, there is in principle another method that probes the effect on band shapes in one-dimensional IR and Raman spectroscopy. This approach, analogous to the evaluation of peak behavior in NMR spectroscopy, is considered next. One-Dimensional Infrared Spectroscopy. Spectral line Figure 7. Fe(CO)3(diene) complexes showing rapid CO ligand shapes are a question of time scale. In order to show the effect scrambling; diene refers to butadiene (BUT), norbornadiene (NBD), of temperature on the spectral line shape, it is most convenient and cyclooctadiene (COD). ff fi 1 to consider the e ect on NMR peaks rst. If two spin = /2 nuclei (e.g., 1H) are uncoupled and give rise to bands with a On the basis of 13C NMR data,25 the barrier to turnstile separation of δν Hz and a Lorentzian half-width (1/2W) in the rotation in Fe(CO) (BUT) was determined to be 8 kcal mol−1, π 3 absence of exchange equal to 1/ T2, then with the usual Bloch which results in an exchange rate that is much too low to have equations the NMR spectrum is easily calculated as a function any effect on the vibrational spectrum. However, Fe- of the exchange rate. For the moment, just consider the (CO)3(NBD) and Fe(CO)3(COD) behave like Fe(CO)5 in extremes of “slow” (i.e., k → 0) and “fast” (k → ∞) exchange: that the 13C NMR spectra show only a single peak for the three In slow exchange, the spectrum shows two Lorentzian bands, carbonyl ligands at all accessible temperatures. Figure 8a 26 each of which is centered at the original peak position but with displays the change in the IR spectrum of Fe(CO)3(COD) half-width (1/2W) increased by k/π according to 1/2W/Hz ≈ in 2-methylpentane in the ν(CO) region. π π 1/ T2 + k/ . However, in fast exchange, the spectrum shows The two low-frequency bands, assigned to the symmetry ≈ ′ ″ only a single peak with the half-width given by 1/2W/Hz 1/ species a and a of the Cs point group, merge as the π π δν 2 δν T2 +( /2k)( ) .IfT2 = 0.5 s and = 20 Hz, then the line temperature is raised. Grevels reasoned that if the CO groups width can be estimated as 1/2W ≈ 0.64 Hz + 630/k for fast rotate very fast, then the complex effectively adopts C − 3v exchange. Thus, with k values in the range 103 to 104 s 1, there symmetry and the a′ and a″ vibrations become e′. However, is one band with a width of 1/2W ≈ 1.3 to 0.7 Hz, which before kinetic data can be extracted from coalescing IR spectra, shows, as is well-known, that in this regime the single coalesced there are several problems to be resolved that concern the band narrows with increasing k. Bloch equations, line shapes, and the relationship between For IR and Raman spectroscopies, the following can be vibrations and torsional energy levels. − stated: Suppose there are two bands, 10 cm 1 apart, each with The Bloch Equations. Considerable doubt has been cast − 1/2W = 1.0 cm 1. Assuming (for the moment) that the Bloch on the use of the Bloch method for vibrational spectra, − equations apply, one can estimate from the above relationships particularly by Strauss27 29. Grevels was well aware of this the magnitude of k to produce coalescence. If k =1010 s−1, then question in his first publications23,24 but assumed that one

4291 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article

point is raised here because it is important to consider such ff e ects in the case of Fe(CO)5, and this will be discussed later. Interacting Vibrations. For metal carbonyls, there is mixing of the C−O stretching vibrations, which greatly complicates the issue. In the paper by Grevels et al.,26 McClung showed the method of taking this into account, and the net result is shown in Figure 8b. The match between experiment (Figure 8a) and theory (Figure 8b) is impressive. It is important, for comparison with Fe(CO)5, to see how this was done. The starting point was to assume that in the absence of exchange, the ν(CO) band positions shifted slightly with temperature in a manner similar to the nonexchanging ’ Fe(CO)3(BUT). McClung s spectrum simulation program was then used to fit the spectra at different temperatures with changing values of the rate constant. The details of the mathematical apparatus are given in the SI. The rate varied from 1.5 × 1011 s−1 at 133 K to 1.54 × 1012 s−1 at 293 K. An Arrhenius plot gave a straight line with an activation energy of 1.1 kcal mol−1. The McClung program generates nonexchanging Voigt profiles for the coalescing bands; see Table 3 in ref 26. For example, the nonexchanging half-widths wG (Gaussian) ″ ∼ −1 and wL (Lorentzian) of the a band at 1948 cm are 6.8 and 0.9 cm−1, respectively, at 133 K and 1.2 and 5.6 cm−1, respectively, at 293 K. − In several elegant experiments, Lear and co-workers32 34 extended these experiments and essentially confirmed Grevels’s conclusions. It is worth mentioning that two authors30,32 have Figure 8. ν(CO) bands of the variable-temperature spectra of suggested a mistake in McClung’s method, but a careful Fe(CO)3(COD) in 2-methylpentane solution between 133 and 293 analysis of the mathematics shows that the supposed error is K: (a) observed; (b) simulated assuming rapid CO site exchange. due only to an unconventional definition and that in fact Reproduced with permission from ref 26. Copyright 1998 American McClung’s method is essentially the same as theirs. Chemical Society. Behavior of Fe(CO)5. What might one expect to observe for a rapid exchange in Fe(CO)5? Compared with the dienes, there is no obvious point-group symmetry to assign to a rapidly could obtain reasonable values for rate constants and barrier exchanging five-coordinate system. However, it is straightfor- heights. This point has been much discussed, and the details ward to extend the (CO) McClung method to a (CO) were summarized by us elsewhere.20 The general conclusion is 3 5 exchanging system, and McClung has provided the appropriate that the method is applicable, but one must be cautious when modification of the method. We are greatly indebted to him. trying to extract accurate data. In fact, two educational 30,31 Figure 9 shows the expected pattern as the rate of the Berry publications show advanced students how to obtain kinetic ν pseudorotation increases. data from the coalescing (CO) bands of Fe(CO)3(COD). Lorentzian Shapes. So far, the discussion has assumed Not surprisingly, the predicted pattern shows coalescence to Lorentzian shapes for the absorption bands. Of course, IR a single band and mimics NMR behavior. It is clear that there bands almost always show a convolution of Lorentz and is a buildup of intensity between the peaks before there is clear Gaussian functions. This can be accommodated by employing moving-together of the peaks. The importance of this extra intensity feature has been mentioned above. Voigt functions. 11 Frequencies and Half-Widths of IR Bands without In addition to their 2D-IR work, Harris and colleagues also Exchange. The application of the Bloch equations assumes carefully examined the FTIR spectra of Fe(CO)5 in n- that the positions and half-widths of the bands in the absence dodecane as a function of temperature and concluded that  of exchange do not alter with a change in conditions, i.e., as the although there were hints of coalescence including some  temperature is raised. For NMR spectra this is true, but as is evidence for buildup of interpeak intensity it was not possible well-known, for IR and Raman spectra these can vary to distinguish satisfactorily between a broadening pair of fi ff dramatically depending on the solvent. Thus, it is necessary Lorentzian pro les and the e ect of exchange based on to include such considerations carefully in any analysis. McClung’s approach (see the SI). Attempts to extract kinetic Contribution from Torsional Energy Levels. data were not really successful, with rate constants “on the It was − − pointed out by Strauss29 that if the torsional barrier vibrational order of 0.1 ps 1”, compared with 0.12 to 0.22 ps 1 from their levels are populated and if the anharmonic coupling between 2D-IR measurements. The real problem is that before there is these vibrations and the ν(CO) stretching vibrations is convincing evidence of coalescence with increasing temper- significant, then the latter may be affected as the temperature ature, Fe(CO)5 decomposes. However, with the advantage of is raised without any reference to exchange. This would make liquid Xe as a solvent and the resultant very high quality FTIR the Grevels approach invalid. Fortunately, for the iron spectra, we believe that there is weak but clear evidence for the tricarbonyl species, DFT calculations show that the ν(CO) buildup of intensity between the peaks, which becomes clearly vibrations are hardly affected as the barrier is climbed.20 This apparent by comparison of spectra at low and high temperature

4292 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article

Figure 11. The 1975−2045 cm−1 section of the temperature- Figure 9. Simulated IR absorption spectra of Fe(CO) in the region 5 dependent IR spectra of Fe(CO) in supercritical xenon in the of the ν(CO) stretching vibrations. The simulation is based on the 5 temperature interval 302 to 386 K recorded at an optical resolution of model of a Berry pseudorotation using the exchange rate constants −1 −1 × 11 × 11 0.5 cm . kexch/s = 0 (blue), 3.17 10 (green), 8.17 10 (red), and 3.17 × 1012 (black). The band maxima 2024.57 and 2002.98 cm−1 and −1 −1 widths wL/cm = 2.58, 3.95 and wG/cm = 2.75, 3.08 apply throughout (L = Lorentzian; G = Gaussian). derived from these data. Given the difficulties of the measurements, the data adhere to a pleasing straight line with the spectral shape predicted using two pseudo-Voigt within the estimated margins of error. The experimentally profiles (Figure 10). determined Arrhenius activation energy was found to be Ea = 2.5 ± 0.4 kcal mol−1. This is in remarkable agreement with the DFT-calculated values ranging from 2.0 to 2.3 kcal mol−1 and is encouraging for the one-dimensional IR technique. The corresponding values of ΔH⧧/(kcal mol−1) and ΔG⧧/(kcal mol−1) are 1.8 ± 0.4 and 3.9 ± 1.6 (experiment) and 1.4 and 3.2 (theory, DFT; see Table 2). The activation energy obtained from the 2D-IR experiments11 was 1.6 ± 0.3 kcal mol−1. The differing experimental values could possibly arise from two factors: (i) as mentioned above, 2D-IR supplies kinetic data between excited vibrational states, and (ii) the solvent, n-dodecane in this case, might influence the kinetics. We have therefore been investigating the interaction between Fe(CO)5 and various solvents as an extension of the Rose- Petruck work,13 and this will be published shortly. However, there are further structural dynamics implications to consider. 20 DFT calculations of the Fe(CO)3(diene) complexes (Figure 7) show that as the barrier is climbed, both low- ′ ″ ″ ′ −1 frequency bands (a and a ) hardly shift. This means that any Figure 10. The a2 and e bands (ca. 2025 and 2003 cm )ofa −3 extra intensity between peaks must be produced by exchange. Fe(CO)5 solution in supercritical Xe (14.67 mol dm ) at (a, c) 301.6 ff K (2054 psi) and (b, d) 386.1 K (6372 psi). (left) Simulated spectra With Fe(CO)5, the observations are di erent. Because of the based on the best fit using two pseudo-Voigt profiles offset 0.1 au change in symmetry in going from the ground state (D3h)to below experimental spectra. Thick black lines (|) indicate the extra the transition state (C4v) via C2v structures, the spectra are intensity in the experimental spectra, greater than that predicted on quite complex and change as the barrier is climbed. the basis of simple band overlap. (right) Experimental (black) and Calculations were therefore carried out for Fe(CO)5 free of simulated (red) spectra shown without offset. The areas under the solvent−solute interactions. The key spectral parameters as a experimental spectra are normalized. function of the energy change as the barrier is climbed are shown in Table 4.36 But can one obtain quantitative data? Figure 11 shows a The calculations resulted in a ground state showing the ′ ″ whole range of IR spectra of Fe(CO)5 in supercritical xenon as expected two IR-active bands (e and a2 ) at 2008 and 2023 a function of temperature. It was noticed that band maxima cm−1, respectively, with an intensity ratio of 1910/1129, and shift less and bands broaden less with increasing temperature two IR-inactive bands (a′), which compare well with fl ′ −1 ″ when the density of the supercritical uid is kept constant experimental values in Xe (e , 2000 cm and a2 , 2024 instead of the pressure of the fluid (see Table S1). cm−1). The calculations indicate that as the barrier is climbed Starting with the same assumptions as employed for COD, and the symmetry changes from D3h through C2v to C4v at the the IR spectra of Fe(CO)5 were simulated which resulted in transition state, a considerable number of new bands should the data shown in Table 3. Figure 12 shows an Arrhenius plot appear, provided that the Kubo parameter remains high (k ≫

4293 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article ν w w w a k Table 3. Band Parameters ( , L, G, ) and Rate Constants ( exch) after Curve Fitting Using the Berry Model of Pseudorotation in the Temperature-Dependent IR Spectra of Fe(CO) at Various Temperatures (T) in Supercritical Xenon at c 5 Constant Density

ν ′ −1 −1 −1 −1b ν ″ −1 −1 −1 −1b 11 −1 T/K (e )/cm wL/cm wG/cm wV/cm (a2 )/cm wL/cm wG/cm wV/cm kexch/(10 s ) 301.6(5) 2003.56(1) 3.91(22) 2.55(12) 4.77 2025.68(2) 2.89(25) 2.09(8) 4.04 1.26(20) 309.7(5) 2003.53(2) 3.89(17) 2.59(12) 4.80 2025.58(2) 2.88(18) 2.11(7) 4.04 1.45(18) 318.3(5) 2003.48(2) 3.88(15) 2.64(11) 4.84 2025.48(2) 2.87(17) 2.13(8) 4.04 1.64(18) 326.8(5) 2003.43(2) 3.87(16) 2.71(6) 4.91 2025.37(2) 2.88(14) 2.13(10) 4.06 1.84(17) 334.0(5) 2003.38(2) 3.86(15) 2.78(6) 4.97 2025.26(3) 2.91(12) 2.16(11) 4.10 1.99(17) 343.3(5) 2003.32(2) 3.82(10) 2.86(4) 5.01 2025.15(2) 2.92(6) 2.18(9) 4.12 2.19(14) 351.5(5) 2003.26(2) 3.85(10) 2.90(6) 5.08 2025.04(3) 2.93(6) 2.18(9) 4.13 2.37(14) 359.5(5) 2003.20(2) 3.82(5) 2.97(6) 5.13 2024.93(3) 2.92(3) 2.18(7) 4.12 2.56(12) 368.0(5) 2003.13(2) 3.82(6) 3.03(7) 5.18 2024.81(3) 2.95(5) 2.18(3) 4.15 2.74(11) 376.4(5) 2003.04(2) 3.78(8) 3.17(9) 5.29 2024.68(3) 2.94(7) 2.25(8) 4.18 2.93(12) 386.0(5) 2002.97(2) 3.79(8) 3.23(7) 5.36 2024.56(3) 2.98(12) 2.21(4) 4.19 3.15(13) aν is the band position, and wL and wG are the Lorentzian and Gaussian contributions, respectively, to the full width at half-maximum of the Voigt ﬁ b 2 2 0.5 c pro le (wV). wV was approximated as 0.5346wL + (0.2166wL + wG ) (see ref 35). Estimated uncertainties are given in parentheses.

halfway between the experimentally observed bands in the spectral region between ca. 2014 and 2017 cm−1.Asthe temperature is raised, these bands are predicted to make an increasing but still very small contribution to the spectrum, and this could in principle add extra intensity between the main peaks and hence make the kinetic interpretation invalid. However, there are two reasons for rejecting this model. In the ﬁrst place, the Kubo parameters for the vibrational levels in these carbonyls have values k ≪ 0, which implies that the molecule is very rapidly switching among the torsional levels. The resulting spectra are not the sum of contributing spectra but the intensity-weighted average of the spectra. (For a discussion of this point, see ref 20.) Second, if this were a Figure 12. Arrhenius plot based on the data given in Table 3. The determining factor, the rate constants would be way out of line, and the activation energy would not be sensible. error bars relate to the uncertainty of kexch over the course of three to four repetitions of curve ﬁtting at individual temperatures. Spectra of Isotopic Fe(CO)5. The exchange between ax- 13 12 13 12 Fe( CO)( CO)4 and eq-Fe( CO)( CO)4 isotopomers will 12 0). The relevance of the Kubo parameter is well-described in mimic the behavior of their isotopologue, Fe( CO)5.In − papers by Strauss and colleagues.27 29 principle, it should therefore be possible to examine the ν(CO) The intensities of these bands will increase with the absorption bands of the isotopic molecules for similar temperature. For instance, in the regions between the ground behavior. Bands 5 and 6 in Figures 3 and 5 are assigned to and transition states, there are bands calculated to lie roughly the axial and equatorial isotopomers. Moreover, because they

E −1 Table 4. Relative Energies ( rel, in kcal mol ) and CO Stretching Frequencies in Fe(CO)5 Calculated at the BP86/AE1 Level along the Intrinsic Reaction Coordinate (IRC, in amu1/2 bohr)

a −1 Harmonic vibrational frequencies (in cm ) are shown in bold type, followed by the symmetry labels of the vibrations (in the D3h, C2v, and C4v point groups for ground, intermediate, and transition states, respectively)/IR intensities (in km mol−1) in normal type. A color code applies to the various vibrational modes to guide the eye. It should be noted that depending on the point-group symmetry, corresponding vibrations can have diﬀerent symmetry labels.

4294 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article are closer in frequency than the main ν(CO) absorption bands barrier for pseudorotation that is consistent with the 12 of Fe( CO)5, they should display this behavior more experimental value. A solvate-assisted mechanism in the obviously. Figure 4 shows this phenomenon to occur in 2- supercritical xenon fluid is unlikely, since any possible Xe− methylpentane, where the bands appear to be coalescing. Fe coordination is of a weak van der Waals-type that leads to Disappointingly, although there is some evidence for band an only marginally lower activation barrier. coalescence in Xe, it is not convincing, and it is certainly not sufficient to produce meaningful kinetic data. ■ ASSOCIATED CONTENT *S Supporting Information ■ EXPERIMENTAL SECTION The Supporting Information is available free of charge on the Spectroscopy. The variable-temperature experiments involving ACS Publications website at DOI: 10.1021/acs.organo- Fe(CO)5 in xenon were carried out at the School of Chemistry of the met.9b00559. Research data supporting this publication can University of Nottingham. Spectra in 2-methylcyclohexane and be accessed at https://doi.org/10.17630/2b3d2f0e-7add-46e0- ̈ krypton were recorded by Grevels and Klotzbucher at the Max- 9b2e-db94fbbbc0e1. Planck-Institut für Bioanorganische Chemie. Fourier transform infrared spectra were recorded at a resolution of 0.5 cm−1 using Energy-factored force field for metal carbonyls, details custom-made miniature high-pressure stainless steel (r.t. to 386 K) on the computer program for the evaluation of the and annealed copper (162 to 316 K) optical cells, which were adapted energy-factored CO force field parameters, the eigen- from published designs and equipped with CaF2 windows of various vector matrix, the wavenumbers of individual CO thicknesses.37 For measurements at and above the critical point, a −3 stretching vibrations, exchange and z matrices, coor- constant density of xenon (14.7 mol dm ) was maintained in the dinates, further computational details, and details of spectroscopic cell. The high-pressure stainless steel gas handling spectral measurements and sample preparation (PDF) manifold and the optical cells connected to it were deoxygenated prior to loading of samples and preparation of solutions. After each Coordinate file (XYZ) temperature change and before each spectral measurement, the optical cells were allowed to equilibrate for 20 min, after which the ■ AUTHOR INFORMATION temperature in solution was constant to within ±0.2 K. No sample degradation was observed below ca. 383 K. Measurements at low Corresponding Author temperature were performed using an annealed Cu cell mounted on a *E-mail: p.portius@sheffield.ac.uk. fi cold nger cooled by a Displex He closed-cycle cryostat and protected ORCID by a high-vacuum shroud equipped with CaF2 windows. Solutions −3 Peter Portius: 0000-0001-8133-8860 were prepared with Fe(CO)5 concentrations on the order of 10 mol dm−3, and the ν(CO) absorption band maxima were kept below Michael W. George: 0000-0002-7844-1696 unity. Author Contributions Computations. Geometries were optimized at the BP86 and ’ F.-W.G. initiated the research and contributed the initial force BP86-D3 levels of DFT (the latter including Grimme s empirical field analysis. M.B. performed the DFT calculations. P.P. dispersion correction), employing the following basis sets: AE1, an augmented (8s7p4d) Wachters’ basis on Fe and the 6-31G(d) basis performed the experimental studies. P.P. and J.J.T. analyzed on C and O; AE2, the same Wachters’ basis on Fe, the aug-cc-pVTZ- the data and wrote the manuscript with the help of all authors. PP basis together with the Stuttgart−Köln RSC-28-MDF relativistic Notes effective core potential on Xe and the 6-311+G(d,p) basis on C and The authors declare no competing financial interest. # O. Starting from the BP86/AE1 transition state for Fe(CO)5, the F.-W.G.: deceased in 2016. intrinsic reaction coordinate (IRC) was followed. Harmonic frequencies were computed analytically for the stationary points as ■ ACKNOWLEDGMENTS well as for selected points on the IRC and are reported without ··· scaling. Energies and frequencies for Fe(CO)5 Xe were corrected for The authors are indebted to Prof. T. E. D. McClung basis-set superposition error (BSSE) using the counterpoise method. (University of Alberta at Edmonton) and Dr. W. E. The BP86-D3/AE2 frequencies were also used to calculate zero-point Klotzbücher (Max-Planck-Institut für Bioanorganische Chem- energies and thermodynamic corrections to enthalpies and free ̈ fi ie, Mulheim an der Ruhr) for the provision of the IR spectrum energies at 298 K. The scan in Figure 6 was obtained by xing the simulation program for fluxional carbonyl complexes and the Fe···Xe distance at selected values and relaxing all of the other 5, parameters at the BP86-D3/AE2 level (including BSSE correction); indicated spectral data (Figure a). M.B. thanks the School of the BP86/AE2 data were obtained by subtracting the -D3 correction Chemistry and EaStCHEM for support. Calculations were from the BP86-D3/AE2 energies at each of the optimized points. performed on a local Opteron cluster maintained by Dr. H. These computations employed the Gaussian suite of programs. See Fruchtl. P.P. thanks the School of Chemistry, University of the SI for full details and references. Nottingham, and the European Commission’s 6th Framework Programme (Grant 502440) for supporting the experimental ■ CONCLUSION work. On the basis of temperature-dependent FTIR spectral ABBREVIATIONS measurements in supercritical xenon solution at a constant ■ density, a reliable value of 2.5 ± 0.4 kcal mol−1 has been BUT, butadiene; COD, cyclooctadiene; DFT, density func- obtained for the activation energy of the intramolecular tional theory; FTIR, Fourier transform infrared; IVR, intra- interchange of CO ligands in Fe(CO)5 according to the molecular vibrational redistribution; NBD, norbornadiene; Berry pseudorotation mechanism. This was enabled by a NMR, nuclear magnetic resonance. quantitative line shape analysis that accounts for the exchange- rate-dependent changes in the absorption bands of the CO ■ REFERENCES fl stretching vibrations. The uxionality of Fe(CO)5 was (1) Mond, L.; Quincke, F. Note on a Volatile Compound of Iron investigated by DFT calculations, which afforded an activation with Carbonic Oxide. J. Chem. Soc., Trans. 1891, 59, 604−607.

4295 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297 Organometallics Article

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4297 DOI: 10.1021/acs.organomet.9b00559 Organometallics 2019, 38, 4288−4297